Precrossed and crossed modules have an important role in homotopy theory and homological algebra. The adjunction between crossed modules and precrossed modules over a fixed group can be seen as a special case of a more general adjunction between internal groupoids and internal reflexive graphs in a Mal'tsev variety. Central extensions with respect to this adjunction are described using the categorical Galois theory. This characterization provides a natural way to define a categorical notion of Peiffer commutator which will be useful, e.g., for establishing a generalized Stallings-Stammbach sequence.